DUBAI (Reuters) - An adviser to Iran's Supreme Leader Ayatollah Ali Khamenei joined the presidential race on Friday, with authorities keen to make the June vote a peaceful contrast to the upheaval that followed the disputed 2009 poll.

Reformist groups have been suppressed or sidelined since then and the next president is likely to be picked from among a handful of politicians known for fealty to Khamenei, minimizing the chances of political rifts leading to post-election chaos.

Lawmaker and former parliament speaker Gholam-Ali Haddad-Adel registered to run, state news agency IRNA reported, becoming the first of a trio of Khamenei loyalists to do so.

Khamenei, who in theory stands above the political fray, is thought to want a reliable follower in the presidency after Mahmoud Ahmadinejad's two turbulent terms - and to thwart any attempt by the outgoing president to promote his own successor.

Allied with Haddad-Adel are former Foreign Minister Ali Akbar Velayati and Tehran mayor Mohammad Baqer Qalibaf - Iranian media say two of them will step aside later in favor of whoever appears to have the best chance of winning the election.

"Our final choice will be announced after the Guardian Council's decision," the semi-official Fars news agency quoted Haddad-Adel as saying after registering, referring to a body which vets applicants before they are allowed to run.

The conservative council, made up of six clerics and six jurists, will publish the final candidate list later this month.

The June 14 vote is a test for Iran after Ahmadinejad's re-election in 2009 ignited the worst street protests in the Islamic Republic's history, badly denting the legitimacy of its entrenched leaders and its hybrid clerical-electoral system.

Khamenei, who has the final say in all major state affairs, endorsed Ahmadinejad's victory, rejecting opposition charges of election fraud. But the president later alienated the supreme leader by pursuing his own policies in often provocative ways.

Among other candidates who registered on Friday was reformist Mohammad Reza Aref, who served as vice-president under former moderate President Mohammad Khatami.

Khatami, who was elected in landslide victories in 1997 and 2001, has not made clear whether he will run this time. Candidate registration started on Tuesday and ends on Saturday.

(Reporting by Zahra Hosseinian; Editing by Alistair Lyon)